Prove $35\sqrt{55}+55\sqrt{77}+77\sqrt{35}+35\sqrt{77}+55\sqrt{35}+77\sqrt{55}\gt 2310$.
The first idea that might sprang to your mind whenever you see square root terms and the inequality is you want to squaring both sides of the inequality and you are expected to finally prove a figure is larger than another figure and you are hence done.